1. Field of the Invention
The present invention relates to electronic components for use in electronic apparatuses such as mobile telephones, and more particularly to a piezoelectric resonator, a production method thereof, and a filter, a duplexer, and a communication device, which include the piezoelectric resonator.
2. Description of the Background Art
Components included in electronic apparatuses such as mobile devices are required to become more compact and lighter. For example, filters for use in mobile devices are required to be compact and accurately adjustable for frequency response.
A known filter, which satisfies the above requirements, includes a piezoelectric resonator (see, for example, pp. 2-4, and FIGS. 3 and 4 of Japanese Laid-Open Patent Publication No. 60-68711).
FIG. 18A is a cross-sectional view showing the basic structure of a conventional piezoelectric resonator. In FIG. 18A, the conventional piezoelectric resonator includes a vibration member 710 provided on a substrate 705. A cavity 704 is formed by partially etching the substrate 705 from its bottom surface using a micro machining method. The vibration member 710 includes a piezoelectric member 701, which is a primary component of the vibration member, and upper and lower electrodes 702 and 703 provided on opposite surfaces of the piezoelectric member 701.
The reason that the hollow cavity 704 is provided in the substrate 705 is to allow the vibration member 710 to vibrate.
Through the upper and lower electrodes 702 and 703 provided on the opposite surfaces of the piezoelectric member 701, electric fields are applied to the vibration member 710 in its thickness direction. This causes the vibration member 710 to vibrate in the thickness direction.
Hereinbelow, an operation of the conventional piezoelectric resonator is described with respect to vibration in the thickness direction perpendicular to an infinite plane. FIG. 18B is a schematic perspective view used for explaining the operation of the conventional piezoelectric resonator. As shown in FIG. 18B, if an electric field is applied between the upper and lower electrodes 702 and 703, electric energy is converted into mechanical energy within the piezoelectric member 701, thereby inducing mechanical vibration. The induced mechanical vibration expands in the thickness direction, so that the piezoelectric member 701 expands and contracts in the same direction as the electric field is applied.
In the case where the thickness of the vibration member 710 is t, the vibration member 710 resonates at a resonance frequency fr1(=v/λ), which corresponds to a wavelength of λ having a relationship with t such that t=λ/2, under the effect of resonant vibration of the piezoelectric member 701 in the thickness direction. Here, v is an average of ultrasonic velocity in materials composing the vibration member 710.
In the structure of the conventional piezoelectric resonator shown in FIG. 18A, the piezoelectric member 701 is allowed to vertically vibrate in the thickness direction because the cavity 704 is provided in the substrate 705.
FIG. 18C is an equivalent circuit diagram of the vibration member 710. As shown in FIG. 18C, the equivalent circuit of the vibration member 710 includes a parallel resonance circuit and a series resonance circuit. Specifically, the series resonance circuit includes a capacitor (C1), an inductor (L1), and a resistor (R1), and the parallel resonance circuit includes a capacitor (C0) connected to the series resonance circuit. Accordingly, the vibration member 710 has a resonance frequency and an anti-resonance frequency. FIG. 18D is a graph showing frequency characteristics of admittance of the equivalent circuit shown in FIG. 18C. As shown in FIG. 18D, the admittance is maximized at a resonance frequency fr1, and minimized at an anti-resonance frequency fa1. Here, the resonance frequency fr1 and the anti-resonance frequency fa1 satisfy the following relationships.
      fr1    =          1              2        ⁢        π        ⁢                              L1            ·            C1                                    fa1    =          fr      ⁢                        1          +                      C1            C0                              
It is possible to realize a compact low-loss filter which utilizes resonant vibration of a piezoelectric member if the conventional piezoelectric resonator is applied to the filter so as to take advantage of the frequency characteristics of the admittance of the vibration member 710.
In the conventional piezoelectric resonator shown in FIG. 18A, the cavity 704 (i.e., a through hole) is provided in the substrate 705, and the vibration member 710 is partially fixed on the substrate, so that the vibration member 710 is allowed to vertically vibrate in the thickness direction above the cavity.
As described above, it is known to provide the cavity 704 in a piezoelectric resonator in order to reliably cause vertical vibration in the thickness direction. In actuality, however, as shown in FIG. 18A, the vibration member 710 is partially fixed on the substrate 705, and therefore the vibration member 710 does not entirely generate free vertical vibration in the thickness direction. This can be said not only of the piezoelectric resonator as shown in FIG. 18A, where the cavity is formed to pass through the bottom surface of the substrate, but also of a piezoelectric resonator in which a cavity is formed by etching a substrate. As described above, in the conventional piezoelectric resonator, the vibration member 710 is partially fixed on the substrate, therefore the vibration member 710 is inhibited from freely vibrating, or vibration energy is caused to partially leak into the substrate. Accordingly, the conventional piezoelectric resonator has a difficulty in achieving a high Q-factor and a wide frequency range (Δf) which corresponds to a difference between the resonant frequency and the anti-resonant frequency.
FIG. 19A is an equivalent circuit diagram of a filter including a piezoelectric resonator. The filter shown in FIG. 19A includes a piezoelectric resonator 711 connected in series between input and output terminals, and a piezoelectric resonator 712 connected in parallel between the input and output terminals. FIG. 19B is a graph showing band-pass characteristics of the filter shown in FIG. 19A. In FIG. 19B, the horizontal axis indicates frequency, and the vertical axis indicates the amount of attenuation.
Similar to the conventional piezoelectric resonator, the piezoelectric resonators 711 and 712 each have a narrow frequency range Δf and a low Q-factor. In this case, the band-pass characteristic of the filter is as indicated by the dotted curve in FIG. 19B. From the dotted curve in FIG. 19B, it is found that in the case of using the piezoelectric resonators 711 and 712 each having a narrow frequency range Δf and a low Q-factor, the passband width of the filter is narrowed, while the loss of the filter is increased. Also, the amount of attenuation at attenuation poles is reduced, resulting in a reduction in steepness of slopes. As such, in the case of using the piezoelectric resonators 711 and 712 each having a narrow frequency range Δf and a low Q-factor, satisfactory filter characteristics cannot be achieved.
In comparison, consider a case where piezoelectric resonators having a wide frequency range Δf and a high Q factor are implemented. In such a case, the pass-band characteristic of the filter is as indicated by the solid curve in FIG. 19B. From the solid curve in FIG. 19B, it is found that in the case of using the piezoelectric resonators having a wide frequency range Δf and a high Q-factor, it is possible to increase the passband width of the filter compared to the case of using the piezoelectric resonators having a narrow frequency range Δf and a low Q factor. Also, the loss of the filter is reduced, and the amount of attenuation at attenuation poles is increased, resulting in an increase in steepness of slopes.